Package org.hipparchus.special
Class BesselJ
java.lang.Object
org.hipparchus.special.BesselJ
- All Implemented Interfaces:
UnivariateFunction
This class provides computation methods related to Bessel
functions of the first kind. Detailed descriptions of these functions are
available in Wikipedia, Abramowitz and
Stegun (Ch. 9-11), and DLMF (Ch. 10).
This implementation is based on the rjbesl Fortran routine at Netlib.
From the Fortran code:
This program is based on a program written by David J. Sookne (2) that computes values of the Bessel functions J or I of real argument and integer order. Modifications include the restriction of the computation to the J Bessel function of non-negative real argument, the extension of the computation to arbitrary positive order, and the elimination of most underflow.
References:
- "A Note on Backward Recurrence Algorithms," Olver, F. W. J., and Sookne, D. J., Math. Comp. 26, 1972, pp 941-947.
- "Bessel Functions of Real Argument and Integer Order," Sookne, D. J., NBS Jour. of Res. B. 77B, 1973, pp 125-132.
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Nested Class Summary
Modifier and TypeClassDescriptionstatic class
Encapsulates the results returned byrjBesl(double, double, int)
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Constructor Summary
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Method Summary
Modifier and TypeMethodDescriptionstatic BesselJ.BesselJResult
rjBesl
(double x, double alpha, int nb) Calculates Bessel functions \(J_{n+alpha}(x)\) for non-negative argument x, and non-negative order n + alpha.double
value
(double x) Returns the value of the constructed Bessel function of the first kind, for the passed argument.static double
value
(double order, double x) Returns the first Bessel function, \(J_{order}(x)\).
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Constructor Details
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BesselJ
public BesselJ(double order) Create a new BesselJ with the given order.- Parameters:
order
- order of the function computed when usingvalue(double)
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Method Details
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value
Returns the value of the constructed Bessel function of the first kind, for the passed argument.- Specified by:
value
in interfaceUnivariateFunction
- Parameters:
x
- Argument- Returns:
- Value of the Bessel function at x
- Throws:
MathIllegalArgumentException
- ifx
is too large relative toorder
MathIllegalStateException
- if the algorithm fails to converge
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value
public static double value(double order, double x) throws MathIllegalArgumentException, MathIllegalStateException Returns the first Bessel function, \(J_{order}(x)\).- Parameters:
order
- Order of the Bessel functionx
- Argument- Returns:
- Value of the Bessel function of the first kind, \(J_{order}(x)\)
- Throws:
MathIllegalArgumentException
- ifx
is too large relative toorder
MathIllegalStateException
- if the algorithm fails to converge
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rjBesl
Calculates Bessel functions \(J_{n+alpha}(x)\) for non-negative argument x, and non-negative order n + alpha.Before using the output vector, the user should check that nVals = nb, i.e., all orders have been calculated to the desired accuracy. See BesselResult class javadoc for details on return values.
- Parameters:
x
- non-negative real argument for which J's are to be calculatedalpha
- fractional part of order for which J's or exponentially scaled J's (\(J\cdot e^{x}\)) are to be calculated. 0 <= alpha < 1.0.nb
- integer number of functions to be calculated, nb > 0. The first function calculated is of order alpha, and the last is of order nb - 1 + alpha.- Returns:
- BesselJResult a vector of the functions \(J_{alpha}(x)\) through \(J_{nb-1+alpha}(x)\), or the corresponding exponentially scaled functions and an integer output variable indicating possible errors
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